Search results for " PD"
showing 10 items of 651 documents
Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds
2021
We prove that if $M$ is a closed $n$-dimensional Riemannian manifold, $n \ge 3$, with ${\rm Ric}\ge n-1$ and for which the optimal constant in the critical Sobolev inequality equals the one of the $n$-dimensional sphere $\mathbb{S}^n$, then $M$ is isometric to $\mathbb{S}^n$. An almost-rigidity result is also established, saying that if equality is almost achieved, then $M$ is close in the measure Gromov-Hausdorff sense to a spherical suspension. These statements are obtained in the ${\rm RCD}$-setting of (possibly non-smooth) metric measure spaces satisfying synthetic lower Ricci curvature bounds. An independent result of our analysis is the characterization of the best constant in the Sob…
Attraction d'ondes pour des systèmes à résonance d'ondes contra-propagatives
2011
Wave attraction in counter-propagating waves systems is a general phenomenon that was first established in Physics in the context of the attraction of the polarization between two counter-propagating waves in optical fibers. This phenomenon has been observed experimentally, and its properties were studied through numerical simulations. The models are Hamiltonian hyperbolic systems of partial differential equations, with time-dependent boundary conditions on a finite interval. The underlying mechanism can be traced back to the existence of singular tori in the corresponding stationary equations. In this work we analyze in detail the simplest example in this family of models. We show that mos…
The fixed angle scattering problem and wave equation inverse problems with two measurements
2019
We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the far field pattern generated by plane waves coming from exactly two opposite directions. This implies that a reflection symmetric potential is uniquely determined by its fixed angle scattering data. We also prove a Lipschitz stability estimate for an associated problem. Motivated by the point source inverse problem in geophysics, we show that a compactly supported potential is uniquely determined from boundary measurements of the waves generated by exactl…
A generalized porous medium equation related to some singular quasilinear problems
2014
Abstract In this paper we study the existence and nonexistence of solutions for a Dirichlet boundary value problem whose model is { − ∑ m = 1 ∞ a m Δ u m = f in Ω u = 0 on ∂ Ω , where Ω is a bounded domain of R N , a m is a sequence of nonnegative real numbers, and f is in L q ( Ω ) , q > N 2 .
Existence of a traveling wave solution in a free interface problem with fractional order kinetics
2021
Abstract In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 α 1 . We turn the free interface problem into a scalar free boundary problem coupled with an integral equation. The main intermediary step is to reduce the scalar problem to the study of a non-Lipschitz vector field in dimension 2. The latter is treated by qualitative topological methods based on the Poincare-Bendixson Theorem. The phase portrait is determined and the existence of a stable manifold at the origin is proved. A significant result is that the settling time to reach the origin is fin…
Effect of the wooden vats on traditional cheese characteristics
2017
Wooden vats have been used for centuries to collect and transform milk by farmers and cheesemakers all over the world. Nowadays, the tree species mostly used to this purpose are Douglas fir and chestnut. The use of wooden vats is mandatory for the production of all PDO Sicilian cheeses, such as Ragusano, Pecorino Siciliano, Piacentinu Ennese and Vastedda della valle del Belìce. In the last years, the wooden vats have been deeply explored for the microbiological characteristics and they are covered by biofilms mainly represented by lactic acid bacteria (LAB) entrapped in a polysaccharide matrix. These microbial associations do not include pathogenic species. Up to date, there are no studies …
Nuovi materiali per celle a combustibile ad ossidi solidi a temperatura intermedia (IT-SOFC): sintesi, caratterizzazione e correlazione struttura-pro…
2014
Pd-Co-Based Electrodes for Hydrogen Production by Water Splitting in Acidic Media
2023
To realize the benefits of a hydrogen economy, hydrogen must be produced cleanly, efficiently and affordably from renewable resources and, preferentially, close to the end-users. The goal is a sustainable cycle of hydrogen production and use: in the first stage of the cycle, hydrogen is produced from renewable resources and then used to feed a fuel cell. This cycle produces no pollution and no greenhouse gases. In this context, the development of electrolyzers producing high-purity hydrogen with a high efficiency and low cost is of great importance. Electrode materials play a fundamental role in influencing electrolyzer performances; consequently, in recent years considerable efforts have b…